4 posts in this series
A simulator that matches history perfectly has only been tested on regimes that already happened. This post prices what that comfort costs, using Lai and Robbins' 1985 regret floor, and shows why neither more logging nor more simulation runs can close the gap.
13 September 2026A scheduled canary test for the failure you already suspect is a second simulator built to agree with you. Feldbaum's 1960 dual control theory supplies the alternative: a control action that regulates the system and keeps testing its own estimates, with no scheduled point where it stops. TCP BBR has run one at internet scale since 2016.
20 September 2026A permanent probe needs a boundary a reviewer can approve once. This post builds it as a discrete-time stochastic control barrier function, then names its gap: bounding how often a system leaves its safe region says nothing about how far it goes. Under a heavy tail, the worst case can run four orders of magnitude past what the reviewer signed.
24 September 2026When does more simulation stop paying, and building the fix become overdue? This post treats the decision as a bounded premium paid once for the right to survive an open-ended, heavy-tailed cost, and derives the threshold. At the base discount rate every tail weight the series has priced clears it, though the lightest tail's margin depends on that rate in a way the heavier tails' margins do not.
27 September 2026